Bounded Connected Components of Polynomial Lemniscates
Complex Variables
2024-10-03 v2 Classical Analysis and ODEs
Abstract
We consider families of polynomial lemniscates in the complex plane and determine if they bound a Jordan domain. This allows us to find examples of regions for which we can calculate the projection of to the Bergman space of the bounded region. Such knowledge has applications to the calculation of torsional rigidity.
Keywords
Cite
@article{arxiv.2312.12603,
title = {Bounded Connected Components of Polynomial Lemniscates},
author = {Adam Kraus and Brian Simanek},
journal= {arXiv preprint arXiv:2312.12603},
year = {2024}
}
Comments
Significant change to Lemma 2.1 and the way it was applied